Arda Halu, Luca Ferretti, Alessandro Vezzani, Ginestra Bianconi
Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed and quenched networks and we show that when the second moment of the average degree diverges the Mott-Insulator phase disappears in the thermodynamic limit. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.
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http://arxiv.org/abs/1203.1566
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